There are two main forms of irony employed in this excellent short story by D. H. Lawrence. The first is situational irony, and we are presented with an example in the very first paragraph. Here the author introduces us to the mother in the story who is undergoing a conflict between appearance and reality:
She had bonny children yet she felt they had been thrust upon her, and she could not love them. They looked at her coldly, as if they were finding fault with her. And hurriedly she felt she must cover up some fault in herself. Yet what it was that she must cover up she never knew. Nevertheless, when her children were present, she always felt the centre of her heart go hard.
The woman appears to love her children, and in fact we are told that everyone else says of her she is a very good mother because she "adores" her children, but in fact, her heart was "a hard little place" that was incapable of loving anyone.
The second type of irony we find is dramatic irony. We, Paul and Uncle Oscar know the source of the money that Paul's mother receives, but she does not. It is clearly ironic that what is a gift of love and a result of care and concern for the mother is responded to with such avaricious greed and rapaciousness. For, we are told that after receiving the first instalment of the money, Paul's mother went that very day to the lawyer to ask for the whole money at once. It is likewise ironic that Paul's mother doesn't realise what Paul is doing to himself until it is too late.